The Metaphysics Research Lab

Center for the Study of Language and Information
Cordura Hall 202
Stanford University
Stanford, CA 94305-4115

Welcome to the web pages of the Metaphysics Research Lab. Whereas physics is the attempt to discover the laws that govern fundamental concrete objects, metaphysics is the attempt to discover the laws that systematize the fundamental abstract objects presupposed by physical science, such as mathematical objects and relations, possible states and events, types (as opposed to tokens), possible and future objects, complex properties, etc. Abstract objects are even needed to understand what may turn out to be scientific fictions (e.g., causality, models) as well as clearcut cases of scientific fictions (e.g., absolute simultaneity, the aether, and phlogiston). The goal of metaphysics, therefore, is to develop a formal ontology, i.e., a formally precise systematization of these abstract objects. Such a theory will be compatible with the world view of natural science if the abstract objects postulated by the theory are conceived as patterns of the natural world.

In our research lab, we have developed such a theory: the axiomatic theory of abstract objects and relations. In many ways, this theory is like a machine for detecting abstract objects (hence the name ‘research lab’), for among the recursively enumerable theorems, there are statements which assert the existence of the abstract objects mentioned above. Moreover, the properties of these abstracta can be formally derived as consequences of the axioms. The theory systematizes ideas of philosophers such as Plato, Leibniz, Frege, Meinong, and Mally. Our results are collated in the document Principia Metaphysica, which is authored by Edward N. Zalta (Ph.D./Philosophy), a Senior Research Scholar at CSLI. An online version of Principia Metaphysica can be found by following the link to The Theory of Abstract Objects (see below). In published work, the theory has been applied to problems in the philosophy of language, intensional logic, the philosophy of mathematics, and the history of philosophy.

sound file icon Welcome Message (272K sound file) (.snd, .au, or .wav)
      (Recorded December 1, 1994)

graphic image of the principles of the theory of abstract objects The Theory of Abstract Objects (Summary and Tutorial)

Computational Metaphysics Web Pages (by Branden Fitelson, Paul E. Oppenheimer, and Edward N. Zalta)

Streaming Video Lecture: Towards Leibniz's Goal of a Computational Metaphysics
by Edward N. Zalta,
Munich Center for Mathematical Philosophy Workshop, June 11, 2011
Slides For the Lecture (in PDF)

Streaming Video: Possible Worlds, the Lewis Principle and the Myth of a Large Ontology
by Edward N. Zalta and Christopher Menzel
Munich Center for Mathematical Philosophy Workshop, June 4, 2011
Slides For the Lecture (in PDF)

Streaming Audio Lecture: A Logically Coherent Ante Rem Structuralism
by Edward N. Zalta and Uri Nodelman
Ontological Dependence Workshop, University of Bristol, February 2011
Slides for the talk.
(This talk was developed into a paper, retitled “Foundations for Mathematical Structuralism,” and in the journal Mind in 2014. Here is a preprint.)

Streaming Video Lecture: Steps Toward a Computational Metaphysics
by Edward N. Zalta and Branden Fitelson
Computing and Philosophy Conference, Oregon State University, August 8, 2003
Slides For the Lecture (in PDF)

thumbnail photo of Ernst MallyErnst Mally icon which could be an image of either Plato or MeinongPlato and Meinong

thumbnail photo of Gottlob FregeGottlob Frege thumbnail photo of Gottfried Wilhelm LeibnizGottfried Wilhelm Leibniz

Personnel iconMetaphysics Research Lab Personnel

Active Collaborators

The following list of personnel are actively working, or have recently collaborated, on the research and development pursued in the Metaphysics Research Lab.